A parallel version of the MOPEX software, which generates mosaics of infrared astronomical images acquired by the Spitzer Space Telescope, extends the capabilities of the prior serial version. In the parallel version, both the input image space and the output mosaic space are divided among the available parallel processors. This is the only software that performs the point-source detection and the rejection of spurious imaging effects of cosmic rays required by Spitzer scientists. This software includes components that implement outlier-detection algorithms that can be fine-tuned for a particular set of image data by use of a number of adjustable parameters. This software has been used to construct a mosaic of the Spitzer Infrared Array Camera Shallow Survey, which comprises more than 17,000 exposures in four wavelength bands from 3.6 to 8 m and spans a solid angle of about 9 square degrees. When this software was executed on 32 nodes of the 1,024-processor Cosmos cluster computer at NASA s Jet Propulsion Laboratory, a speedup of 8.3 was achieved over the serial version of MOPEX. The performance is expected to improve dramatically once a true parallel file system is installed on Cosmos.